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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
If n is a three-digit prime number and j is an integer, which of the
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10 Jun 2021, 22:08
10 Jun 2021, 22:08
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If n is a three-digit prime number and j is an integer, which of the following is NOT a possible value of k, where k is the smallest positive integer such that n – 5j = k?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If n is a three-digit prime number and j is an integer, which of the
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13 Jun 2021, 02:04
13 Jun 2021, 02:04
1
n – 5j = k
=> n = 5j + k
and we know that n is a three-digit prime number and j is an integer
Now, if k is a number such that k and 5j have any factor apart from 1 common then it is easy to prove that n will not be prime in that case
If we have take option number E, k = 5 then we have
n = 5j + 5 = 5 *(j + 1)
Now, n becomes a multiple of 5 and j+1 which is NOT possible as n is a prime number
So, k cannot be 5
So, answer will be E
Hope it helps!
=> n = 5j + k
and we know that n is a three-digit prime number and j is an integer
Now, if k is a number such that k and 5j have any factor apart from 1 common then it is easy to prove that n will not be prime in that case
If we have take option number E, k = 5 then we have
n = 5j + 5 = 5 *(j + 1)
Now, n becomes a multiple of 5 and j+1 which is NOT possible as n is a prime number
So, k cannot be 5
So, answer will be E
Hope it helps!
gmatclubot
Re: If n is a three-digit prime number and j is an integer, which of the [#permalink]
13 Jun 2021, 02:04
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